Subgroups — #13094056

Order 1504.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625354	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625337	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625336	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625325	C₂	1	1	yes	maximal, characteristic, complemented
7	#10625324	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	D₁₈₈	—	2	1	no	—
11	D₁₈₈	C₂²	1	1	yes	characteristic
12	C₄×D₄₇	—	2	1	no	—
13	C₄×D₄₇	—	2	1	no	—
14	C₄×D₄₇	C₂²	1	1	yes	characteristic
15	Dic₉₄	—	2	1	no	—
16	Dic₉₄	C₂²	1	1	yes	characteristic
17	C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×D₄₇	—	2	1	no	—
20	C₂×D₄₇	D₄	1	1	yes	characteristic
21	C₄×C₄₇	—	2	1	no	—
22	C₄×C₄₇	—	2	1	no	—
23	C₄×C₄₇	C₂³	1	1	yes	characteristic
24	Dic₄₇	—	2	1	no	—
25	Dic₄₇	D₄	1	1	yes	characteristic
26	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
27	D₄₇	—	2	1	no	—
28	D₄₇	—	4	1	no	—
29	C₄₇	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	47	1	no	maximal, Sylow
31	#41	—	47	1	no	—
32	C₂×Q₈	—	47	1	no	—
33	Q₁₆	—	47	1	no	—
34	Q₁₆	D₄₇	1	1	yes	characteristic, complemented
35	SD₁₆	—	47	1	no	—
36	SD₁₆	—	47	1	no	—
37	M₁₆	—	47	1	no	—
38	Q₈	—	47	1	no	—
39	Q₈	—	94	1	no	—
40	Q₈	C₂×D₄₇	1	1	yes	characteristic
41	Q₈	C₂×D₄₇	1	1	yes	characteristic
42	D₄	—	47	1	no	—
43	D₄	—	94	1	no	—
44	C₂×C₄	—	47	1	no	—
45	C₂×C₄	—	94	1	no	—
46	C₂×C₄	—	94	1	no	—
47	C₈	—	47	1	no	—
48	C₈	C₂×D₄₇	1	1	yes	characteristic
49	C₂²	—	47	1	no	—
50	C₂²	—	94	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	47	1	no	—
54	C₄	—	94	1	no	—
55	C₄	C₂²×D₄₇	1	1	yes	characteristic
56	C₂	—	94	1	no	—
57	C₂	—	188	1	no	—
58	C₂	D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₇
commutator, cosocle	C₄×C₄₇	C₂³
Frattini	C₄	C₂²×D₄₇
Fitting	Q₁₆×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₄
prime radical	#10625354	C₂
hypercenter	Q₁₆	D₄₇
hypocenter	C₄₇	#137
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. Q₈×D₄₇	C₂	semidirect
3. Q₁₆×C₄₇	C₂	semidirect
4. #10625337	C₂	semidirect
5. #10625336	C₂	semidirect
6. #10625325	C₂	semidirect
7. #10625324	C₂	semidirect
29. C₄₇	#137	semidirect
34. Q₁₆	D₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10625354	2
Q₈×D₄₇	2
Q₁₆×C₄₇	2
#10625337	2
#10625336	2
#10625325	2
#10625324	2
#137	47